Question

given the triangle
, find the area of the triangle. round your final answer to 4 decimal places.
area =
units²
question help:
video

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The semi - perimeter formula is \(s=\frac{a + b+ c}{2}\), where \(a = 40\), \(b = 12\), \(c = 31\).
\(s=\frac{40 + 12+31}{2}=\frac{83}{2}=41.5\)

Step2: Use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \(s = 41.5\), \(a = 40\), \(b = 12\), \(c = 31\) into the formula.
\(A=\sqrt{41.5(41.5 - 40)(41.5 - 12)(41.5 - 31)}\)
\(=\sqrt{41.5\times1.5\times29.5\times10.5}\)
First, calculate \(41.5\times1.5 = 62.25\), \(29.5\times10.5=309.75\)
Then \(62.25\times309.75 = 19280.4375\)
\(A=\sqrt{19280.4375}\approx138.8536\)

Answer:

\(138.8536\)